Authors: Richard A. O'Keefe, L.Damas, V.S.Costa and Markus
Triska
An association list as implemented by this library is a
collection of unique keys that are associated to values.
Keys must be ground, values need not be.
An association list can be used to fetch elements via their
keys and to enumerate its elements in ascending order of their
keys.
This library uses AVL trees to implement association lists.
This means that
- inserting a key
- changing an association
- fetching a single element
are all O(log(N)) worst-case (and
expected) time operations, where
N denotes the number of elements in the association list.
The logarithmic overhead is often acceptable in practice. Notable
advantages of association lists over several other methods are:
library(assoc) is written entirely in Prolog, making it
portable to other systems- the interface predicates fit the declarative nature of Prolog,
avoiding destructive updates to terms
- AVL trees scale very predictably and can be used to represent sparse
arrays efficiently.
An association list is created with one of the following
predicates:
- [semidet]empty_assoc(?Assoc)
- Is true if Assoc is the empty association list.
- [det]list_to_assoc(+Pairs,
-Assoc)
- Create an association from a list Pairs of Key-Value pairs.
List must not contain duplicate keys.
- Errors
domain_error(unique_key_pairs, List) if List contains
duplicate keys
- [det]ord_list_to_assoc(+Pairs,
-Assoc)
- Assoc is created from an ordered list Pairs of
Key-Value pairs. The pairs must occur in strictly ascending order of
their keys.
- Errors
domain_error(key_ordered_pairs, List) if pairs are not
ordered.
An association list can be queried with:
- [semidet]get_assoc(+Key,
+Assoc, -Value)
- True if Key-Value is an association in Assoc.
- [semidet]get_assoc(+Key,
+Assoc0, ?Val0, ?Assoc, ?Val)
- True if Key-Val0 is in Assoc0 and Key-Val
is in Assoc.
- [semidet]max_assoc(+Assoc,
-Key, -Value)
- True if Key-Value is in Assoc and Key
is the largest key.
- [semidet]min_assoc(+Assoc,
-Key, -Value)
- True if Key-Value is in assoc and Key
is the smallest key.
- [nondet]gen_assoc(?Key,
+Assoc, ?Value)
- True if Key-Value is an association in Assoc.
Enumerates keys in ascending order on backtracking.
- See also
- get_assoc/3.
Elements of an association list can be changed and inserted with:
- [det]put_assoc(+Key,
+Assoc0, +Value, -Assoc)
- Assoc is Assoc0, except that Key is
associated with Value. This can be used to insert and change
associations.
- [semidet]del_assoc(+Key,
+Assoc0, ?Value, -Assoc)
- True if Key-Value is in Assoc0. Assoc
is Assoc0 with
Key-Value removed.
- [semidet]del_min_assoc(+Assoc0,
?Key, ?Val, -Assoc)
- True if Key-Value is in Assoc0 and Key
is the smallest key. Assoc is
Assoc0 with Key-Value removed. Warning: This will
succeed with no bindings for Key or Val if Assoc0
is empty.
- [semidet]del_max_assoc(+Assoc0,
?Key, ?Val, -Assoc)
- True if Key-Value is in Assoc0 and Key
is the greatest key. Assoc is
Assoc0 with Key-Value removed. Warning: This will
succeed with no bindings for Key or Val if Assoc0
is empty.
Conversion of (parts of) an association list to lists is
possible with:
- [det]assoc_to_list(+Assoc,
-Pairs)
- Translate Assoc to a list Pairs of Key-Value
pairs. The keys in
Pairs are sorted in ascending order.
- [det]assoc_to_keys(+Assoc,
-Keys)
- True if Keys is the list of keys in Assoc. The
keys are sorted in ascending order.
- [det]assoc_to_values(+Assoc,
-Values)
- True if Values is the list of values in Assoc. Values
are ordered in ascending order of the key to which they were associated. Values
may contain duplicates.
Further inspection predicates of an association list and its elements
are:
- [semidet]is_assoc(+Assoc)
- True if Assoc is an association list. This predicate checks
that the structure is valid, elements are in order, and tree is balanced
to the extent guaranteed by AVL trees. I.e., branches of each subtree
differ in depth by at most 1. Does not validate that keys are
sufficiently instantiated to ensure the tree remains valid if a key is
further instantiated.
- [semidet]map_assoc(:Pred,
+Assoc)
- True if Pred(Value) is true for all values in Assoc.
- [semidet]map_assoc(:Pred,
+Assoc0, ?Assoc)
- Map corresponding values. True if Assoc is Assoc0
with Pred applied to all corresponding pairs of of values.
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